I have a Galaxy Nexus and I live in Belgium (so my phone is not locked to a specific carrier). The Android version is still 4.0.4 and when I go the system update menu, it doesn't do anything, no OTA update. I thought the version 4.1 or even 4.1.1 was available. How can I update it 'officially'?

Of course, I already searched but I only found update packages that I'm not sure I can trust.

when open Settings -> About -> System updates. You should see something like "Last checked for update on 1/1/1970"

click "Check now" button

if you didn't receive update yet, repeat this procedure from first
step few more times (I've succeeded after second attempt). You could also try to replace step 7 by step 1.

All this sounds very strange for me, but I've tried some separate parts of this sequence many times before and it didn't work. Yesterday I've repeat all 8 step exactly as them written above, two time in a row - and I've finally get Jelly Bean on my Galaxy Nexus (I have yakjuxw firmware).

Your carrier hasn't released the update to their customers yet. Check their support website or call their support to ask.

If you have ever rooted your phone and removed and of the systems applications, which includes bloatware apps like Facebook that come preinstalled, you cannot get OTA updates as your phone's system won't match the update anymore and so it won't install.

p.2 is incorrect, OTA updates come no matter if you have modified your system or not. the only difference is the error message, which appears during the installation. so get can get OTA, just cannot install.
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lenikMay 16 '12 at 15:14

@lenik: A distinction without a difference...
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LogosMay 16 '12 at 18:32

ok but for me OTA updates don't come at all and I didn't flash or modify my ROM.
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JafarMay 22 '12 at 11:16

@jafar: part 2 of my answer doesn't have anything to do with flashing or modifying your ROM, unless you count removing apps as modifying the ROM.
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LogosMay 22 '12 at 13:11

No I don't. I have the stock ROM, not rooted and not modified and independent of any carrier...
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JafarMay 23 '12 at 8:22

Maybe wait, I had a Nexus One and my phone get OTA three or four month after the Google release, because of my carrier.
But you can get the ZIP file of the OTA package and make a manual install.
You can find the file on XDA I think.